Sensitivity analysis in probabilistic discrete graphical models is usually conducted by
varying one probability at a time and observing how this affects output probabilities of
interest. When one probability is varied, then others are proportionally covaried to respect
the sum-to-one condition of probabilities. The choice of proportional covariation is justified
by multiple optimality conditions, under which the original and the varied distributions are
as close as possible under different measures. For variations of more than one parameter
at a time and for the large class of discrete statistical models entertaining a regular
monomial parametrisation, we demonstrate the optimality of newly defined proportional
multi-way schemes with respect to an optimality criterion based on the I-divergence. We
demonstrate that there are varying parameters’ choices for which proportional covariation
is not optimal and identify the sub-family of distributions where the distance between
the original distribution and the one where probabilities are covaried proportionally is
minimum. This is shown by adopting a new geometric characterization of sensitivity
analysis in monomial models, which include most probabilistic graphical models. We also
demonstrate the optimality of proportional covariation for multi-way analyses in Naive
Bayes classifiers.